Dynamic system with no equilibrium and its chaos anti-synchronization

Abstract

Recently, systems with chaos and the absence of equilibria have received a great deal of attention. In our work, a simple five-term system and its anti-synchronization are presented. It is special that the system has a hyperbolic sine nonlinearity and no equilibrium. Such a system generates chaotic behaviours, which are verified by phase portraits, positive Lyapunov exponent as well as an electronic circuit. Moreover, the system displays multistable characteristic when changing its initial conditions. By constructing an adaptive control, chaos anti-synchronization of the system with no equilibrium is obtained and illustrated via a numerical example.

Fuzzy Synchronization of Chaotic Systems with Hidden Attractors

“…Most of the time, researchers focus on solving the problem of synchronizing systems with perturbations and unknown system parameters. Another used control is adaptive control with complete error or anti-synchronization, where they focus on the time of convergence of the error in the synchronization [ 29 ] or the problem where the system parameters are unknown [ 30 , 31 , 32 , 33 , 34 ]. Another control proposal is the fixed-time synchronization observer , which emphasizes the time of convergence of the error in the synchronization under complete error [ 35 ].…”

A Family of 1D Chaotic Maps without Equilibria

“…Thus, from the point of view of applications, the ideal chaotification method ensures that the system is chaotic, but at the same time, there are no fixed points. The works dealing with this problem concern continuous systems for which the above-mentioned problems occur [19][20][21][22][23][24][25], or for discrete maps, mainly piecewise linear ones [26][27][28][29][30][31][32]. Thus, in work [19], the authors presented a 3D dynamical system, which, apart from the lack of fixed points, is characterized by the coexistence of a limit cycle and torus.…”

“…Another chaotic fractional system is also discussed in [23], where apart from the new dynamical system, its synchronization was also presented. In [24], a continuous 3D chaotic dynamical system with no equilibrium and its chaos anti-synchronization was presented. In turn, in [25], the authors present a novel continuous chaotic system without equilibrium.…”

Chaotic Dynamics by Some Quadratic Jerk Systems

“…Recently, researchers have proposed many dynamical systems with hidden attractors, see [20,25,[28][29][30][31][32][33]. Hidden attractors may be found in the following three families: (1) systems without equilibrium, see [23,[34][35][36][37][38][39];…”